I’m Harry Altman. I do strange sorts of math.
Posts I’d recommend:
A summary of Savage’s foundations for probability and utility—if the arguments used to ground probability and utility seem circular to you, here’s a non-circular way of doing it.
Sniffnoy
Karma: 4,079
Immediately before it, actually.
Didn’t Scott just outright concede the argument? (He didn’t; I checked.)
Yikes, this doesn’t seem to contradict many-worlds at all. Many-worlds doesn’t claim worlds don’t interfere with each other; if it did, it’d be falsified by just the two-slit experiment, no need for this complication.
If being a skeptic is the opposite of being a contrarian, your three “slam dunks” won’t distinguish very well—unless you’re assuming we’ve already established the person is a contrarian? Many-worlds seems to be pretty mainstream these days. And as for atheism and P-zombies, doesn’t naturalism/materialism generally go along with skepticism? I think this forces the question of just who you’re talking about being contrary to.
Because one of these allows you to make predictions, and the other doesn’t. Saying “fire has a cause, and I’m going to call it ‘phlogiston’!” doesn’t tell you anything about fire, it’s just a relabeling. Now, if you make enough observations, maybe you’ll eventually conclude that “phlogiston is the absence of oxygen” (even though this isn’t really correct), but at that point you can throw out the label “phlogiston”. Contrariwise, if you say “oxidization causes fire”, where “oxygen” is a previously known thing with known properties, then this allows you to actually make predictions about fire. E.g. the fact a candle in a sufficiently small closed space will go out before it melts, but not necessarily if there’s a plant in there too. One pays rent, the other doesn’t.
Ah, true.
But you can only predict it if you already know that a gain of phlogiston refines iron; if you don’t, you can only observe it afterward and write it down as a property of phlogiston.
If you don’t know anything about oxygen or phlogiston beforehand, then, sure, they’re pretty much equally predictive, i.e., not very much. But if “oxygen” is not in fact just an arbitrary label as “phlogiston” is, but in fact something you’re already working with in other ways, then they’re not symmetric.
Also as Nick Tarleton points out below there are other asymmetries, though those are not so much in the predictive power.
That’s what I just said.
This seems like a special case of the more general “just one can’t hurt” (whatever the current level) way of thinking. I don’t know any name for this but I guess you could call it something like the “non-Archimedean bias”?
Also, alexflint, you mean “negation”, not “converse”.
An interesting application of near/far:
Can’t we just define “blue” or “blueness” or what have you to be an equivalence class and be done with it?
OK, but it’s not too hard to describe what makes a thing blue. The only obvious sticking point is who’s standard of blueness we’re using. Perhaps a “blueness function” would be better than an equivalence class of all things blue, then. Regardless, determining whether or not a given thing is blue doesn’t seem to be what the OP is asking about; I’m suggesting that this suffices.
Agreed. Best is if you can learn something well enough that even if you don’t remember it, you can rederive it; but usually good enough is learning something well enough that you can do it if you’ve got a textbook to remind you.
Since noone’s mentioned it yet, Rendevous with Rama. You really don’t want to touch the sequels, though.
“Generalizing from One Example” and “Reference Class of the Unreferenceclassable” links are both broken.
(Side note: I find myself often trying to find a way to express grasp/control as a pair, because really the two are the same. If you really grasp something, you should be able to control it, at least in principle.)
Well, anything mathematical would be an exception to that, at the least.
OK but that’s not really what “control” normally means, is it? “Manipulate” might be a better word here.
I think you’re really failing to grasp the content of the unique factorization theorem here. Firstly we don’t think about factored numbers as products of primes up to permutation, we think of them as products of distinct prime powers (up to permutation, I suppose—but it’s probably better here to just take a commutative viewpoint and not regard “up to permutation” as worth specifying). But more importantly, you need to take a multiary view of multiplication here, not a binary one. 1 is the empty product, so in particular, it is the product of no primes, or the product of each prime to the 0th power. That is its unique prime factorization. To take 1 as a prime would be like having bases for vector spaces include 0. Almost exactly like it—if we take the Z-module of positive rationals under multiplication, the set of primes forms a free basis; 1 is the zero element.
On parsimony:
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
--John von Neumann, at the first national meeting of the Association for Computing Machinery
I have to point out, you’ve made a mistake of terminology here, one frequently pointed out at Language Log. You seem to have used “passive voice” to mean “construction that is vague as to agency”. It’s important to note weaseling, as you point out, but the use of passive voice isn’t a good heuristic for that. Consider your own example of “Unreliable elements were subjected to an alternative justice process”; little of the weaseliness comes from the use of the passive. It wouldn’t be much less weaselly if written as “When dealing with such unreliable elements, those responsible apply an alternative justice process.” Who’s responsible? I dunno.